Tourist in MSN

There are some very good tutorials on youtube on how to rebuild some things on a bike. But there are some bad ones too. The best way for someone new is to watch 3 or 4 or 5 videos, take notes and do what most of the videos say. Usually the bad videos are suggesting things that others are not suggesting, so that is why I suggest watching several on each topic. Some cone wrenches for the hub are generally not too expensive along with some good grease, you would have to get the right size wrenches. And you probably would want a freewheel puller too, there are different ones for different freewheels.

If the bottom bracket is cup and cone, you might be able to have a shop replace it with a newer cartridge unit. The reason I suggest that is the tools to rebuild and re-grease an older cup and cone bottom bracket might cost as much as having a shop put on a new one.

From a photo, you can't tell if the gears and chain are too worn or if they would need replacing on the Briggs but the range of gears shown in the photos would be much better than the Fox for touring.

There are some good articles on the basics of bicycle parts and repair at this web site. The person that started the website died several years ago but others are occasionally making updates to it.
https://www.sheldonbrown.com/repairs.html

It is pretty easy to fix things on a British bike and this appears to be British. French and some others used threaded parts that are now much harder to find.
https://www.ellisbriggscycles.co.uk/

If you look at the Briggs again, look at the tire size on the tires and write it down. It might say something like (622X32).